Finite Group Databasebeta

← C37×#25956 #22647209

Subgroups — C37×#25956 #22647209

Order 9472.

986 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#478C211yesmaximal, characteristic, complemented
2C2×C37×#416C211yesmaximal, characteristic
3C37×#2441C211yesmaximal, characteristic, complemented
4C37×#2339C211yesmaximal, characteristic
5C37×#2095C211yesmaximal, characteristic, complemented
6C37×#2068C211yesmaximal, characteristic, complemented
7C37×#2066C211yesmaximal, characteristic, complemented
8C37×#2026C211yesmaximal, characteristic, complemented
9C37×#1862C211yesmaximal, characteristic, complemented
10C37×#1862C211yesmaximal, characteristic, complemented
11C37×#1854C211yesmaximal, characteristic, complemented
12C37×#1850C211yesmaximal, characteristic, complemented
13C37×#1808C211yesmaximal, characteristic, complemented
14C37×#1802C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, characteristic
16C22×#41×C37C2211yescharacteristic
17C23×C8×C37C2211yescharacteristic
18C2×#125×C37C2211yescharacteristic
19C2×C4×D4×C37C2211yescharacteristic
20C2×C4×D4×C37C2211yescharacteristic
21C2×#117×C37C2211yescharacteristic
22C37×#478—24no—
23C2×#107×C37C2211yescharacteristic
24C2×#107×C37C2211yescharacteristic
25C2×#107×C37C2211yescharacteristic
26C2×#106×C37C2211yescharacteristic
27C2×C4⋊C8×C37C2211yescharacteristic
28C2×C4⋊C8×C37C2211yescharacteristic
29C37×#416—24no—
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C37×#399—21no—
40C37×#396—21no—
41C37×#391C2211yescharacteristic
42C37×#391C2211yescharacteristic
43C37×#389—21no—
44C37×#389C2211yescharacteristic
45C37×#389C2211yescharacteristic
46C37×#387—21no—
47C37×#386—21no—
48C37×#386—21no—
49C37×#384C2211yescharacteristic
50C37×#381—21no—
51C37×#380C2211yescharacteristic
52C37×#380C2211yescharacteristic
53C4×C22⋊C4×C37C2211yescharacteristic
54C2×#95×C37—21no—
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C2×#41×C37—22no—
62C2×#41×C37—22no—
63C2×#41×C37—22no—
64C2×#41×C37—41no—
65C2×#41×C37—41no—
66C2×#41×C37Q814yes—
67C22×Q8×C37C2311yescharacteristic
68C22×D4×C37—21no—
69C22×D4×C37C2311yescharacteristic
70C23×C4×C37—21no—
71C23×C4×C37—21no—
72C23×C4×C37—21no—
73C23×C4×C37C2311yescharacteristic
74C22×C8×C37—22no—
75C22×C8×C37—22no—
76C22×C8×C37—41no—
77C22×C8×C37C2311yescharacteristic
78C22×C8×C37C2311yescharacteristic
79C22×C8×C37C2311yescharacteristic
80C22×C8×C37C2311yescharacteristic
81#125×C37—22no—
82#125×C37—41no—
83C4×D4×C37—22no—
84C4×D4×C37—22no—
85C4×D4×C37—41no—
86C4×D4×C37—41no—
87#117×C37—22no—
88#117×C37—41no—
89C2×C4⋊C4×C37—21no—
90C2×C4⋊C4×C37—21no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37C2311yescharacteristic
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C22⋊C4×C37—21no—
102C2×C22⋊C4×C37—21no—
103C2×C22⋊C4×C37—21no—
104C2×C22⋊C4×C37—21no—
105C2×C22⋊C4×C37—21no—
106C2×C22⋊C4×C37D411yescharacteristic
107C2×C22⋊C4×C37D411yescharacteristic
108C2×C42×C37—21no—
109C2×C42×C37C2311yescharacteristic
110C2×C42×C37C2311yescharacteristic
111#107×C37—22no—
112#107×C37—41no—
113#107×C37—41no—
114#106×C37—22no—
115C4⋊C8×C37—22no—
116C4⋊C8×C37—41no—
117#103×C37—22no—
118#103×C37—22no—
119#103×C37—41no—
120#103×C37—41no—
121#102×C37—22no—
122#102×C37—22no—
123#102×C37—22no—
124#102×C37D414yes—
125C22⋊C8×C37—22no—
126#95×C37—21no—
127#95×C37—21no—
128#95×C37—21no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37—21no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37D411yescharacteristic
135#95×C37D411yescharacteristic
136C24×C37—21no—
137C24×C37C2×D411yescharacteristic
138#41×C37—28no—
139#41×C37—44no—
140#41×C37—44no—
141#41×C37—44no—
142C2×Q8×C37—21no—
143C2×Q8×C37—21no—
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37C2×Q812yes—
148C2×D4×C37—24no—
149C2×D4×C37—21no—
150C2×D4×C37—21no—
151C2×D4×C37—21no—
152C2×D4×C37—42no—
153C2×D4×C37—42no—
154C2×D4×C37C2×D412yes—
155C2×D4×C37C2×Q812yes—
156C2×D4×C37#4112yes—
157C22×C4×C37—21no—
158C22×C4×C37—21no—
159C22×C4×C37—21no—
160C22×C4×C37—21no—
161C22×C4×C37—21no—
162C22×C4×C37—21no—
163C22×C4×C37—24no—
164C22×C4×C37—21no—
165C22×C4×C37—21no—
166C22×C4×C37—21no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—42no—
170C22×C4×C37—42no—
171C22×C4×C37—42no—
172C22×C4×C37—42no—
173C22×C4×C37—42no—
174C22×C4×C37—42no—
175C22×C4×C37—81no—
176C22×C4×C37—81no—
177C22×C4×C37C2×D411yescharacteristic
178C22×C4×C37C2×D411yescharacteristic
179C22×C4×C37C2×D411yescharacteristic
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2×Q812yes—
183C22×C4×C37#4112yes—
184C22×C4×C37C2411yescharacteristic
185C2×C8×C37—21no—
186C2×C8×C37—21no—
187C2×C8×C37—21no—
188C2×C8×C37—21no—
189C2×C8×C37—21no—
190C2×C8×C37—21no—
191C2×C8×C37—21no—
192C2×C8×C37—21no—
193C2×C8×C37—21no—
194C2×C8×C37—21no—
195C2×C8×C37—21no—
196C2×C8×C37—44no—
197C2×C8×C37C2×D412yes—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—21no—
201C4⋊C4×C37—21no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—21no—
205C4⋊C4×C37—21no—
206C4⋊C4×C37—21no—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37—42no—
210C4⋊C4×C37—42no—
211C4⋊C4×C37—42no—
212C4⋊C4×C37—42no—
213C4⋊C4×C37—81no—
214C4⋊C4×C37—81no—
215C4⋊C4×C37C2×D412yes—
216C22⋊C4×C37—22no—
217C22⋊C4×C37—41no—
218C22⋊C4×C37—42no—
219C22⋊C4×C37—42no—
220C22⋊C4×C37—42no—
221C22⋊C4×C37—81no—
222C22⋊C4×C37—81no—
223C42×C37—21no—
224C42×C37—21no—
225C42×C37—21no—
226C42×C37—21no—
227C42×C37—42no—
228C23×C37—22no—
229C23×C37—21no—
230C23×C37—22no—
231C23×C37—22no—
232C23×C37—21no—
233C23×C37—21no—
234C23×C37—21no—
235C23×C37—21no—
236C23×C37—21no—
237C23×C37—41no—
238C23×C37—41no—
239C23×C37—41no—
240C23×C37—41no—
241C23×C37C22⋊Q812yes—
242C23×C37C22×D411yescharacteristic
243Q8×C37—22no—
244Q8×C37—22no—
245Q8×C37—41no—
246Q8×C37—41no—
247D4×C37—22no—
248D4×C37—22no—
249D4×C37—22no—
250D4×C37—48no—
251D4×C37C22⋊Q814yes—
252C2×C4×C37—21no—
253C2×C4×C37—21no—
254C2×C4×C37—21no—
255C2×C4×C37—21no—
256C2×C4×C37—22no—
257C2×C4×C37—22no—
258C2×C4×C37—22no—
259C2×C4×C37—22no—
260C2×C4×C37—22no—
261C2×C4×C37—21no—
262C2×C4×C37—21no—
263C2×C4×C37—22no—
264C2×C4×C37—21no—
265C2×C4×C37—21no—
266C2×C4×C37—21no—
267C2×C4×C37—21no—
268C2×C4×C37—21no—
269C2×C4×C37—21no—
270C2×C4×C37—21no—
271C2×C4×C37—48no—
272C2×C4×C37—41no—
273C2×C4×C37—41no—
274C2×C4×C37—41no—
275C2×C4×C37—41no—
276C2×C4×C37—41no—
277C2×C4×C37—41no—
278C2×C4×C37—41no—
279C2×C4×C37—41no—
280C2×C4×C37—41no—
281C2×C4×C37—41no—
282C2×C4×C37—41no—
283C2×C4×C37—41no—
284C2×C4×C37—41no—
285C2×C4×C37—41no—
286C2×C4×C37—41no—
287C2×C4×C37—41no—
288C2×C4×C37—41no—
289C2×C4×C37—41no—
290C2×C4×C37—41no—
291C2×C4×C37—84no—
292C2×C4×C37—84no—
293C2×C4×C37C22⋊Q812yes—
294C2×C4×C37#13512yes—
295C2×C4×C37C22×D411yescharacteristic
296C2×C4×C37C22×Q811yescharacteristic
297C2×C4×C37C2×#4111yescharacteristic
298C2×C4×C37C2×#4111yescharacteristic
299C2×C4×C37H(5,𝔽2)11yescharacteristic
300C2×C4×C37H(5,𝔽2)11yescharacteristic
301C8×C37—22no—
302C8×C37—41no—
303C8×C37—41no—
304C8×C37—41no—
305#25956C3711yesmaximal, characteristic, direct product factor, Sylow
306C22×C37—22no—
307C22×C37—22no—
308C22×C37—22no—
309C22×C37—24no—
310C22×C37—42no—
311C22×C37—42no—
312C22×C37—42no—
313C22×C37—41no—
314C22×C37—41no—
315C22×C37—42no—
316C22×C37—42no—
317C22×C37—41no—
318C22×C37—41no—
319C22×C37—42no—
320C22×C37C2×C22⋊Q811yescharacteristic
321C22×C37D4211yescharacteristic
322C22×C37#54611yescharacteristic
323C22×C37C2×#13511yescharacteristic
324C22×C37#57511yescharacteristic
325C22×C37#57611yescharacteristic
326C22×C37#57811yescharacteristic
327C4×C37—22no—
328C4×C37—22no—
329C4×C37—42no—
330C4×C37—41no—
331C4×C37—41no—
332C4×C37—42no—
333C4×C37—41no—
334C4×C37—81no—
335C4×C37—81no—
336C4×C37—81no—
337C4×C37—81no—
338C4×C37—81no—
339C4×C37C2×C22⋊Q811yescharacteristic
340C4×C37#54311yescharacteristic
341C4×C37#54611yescharacteristic
342C4×C37#55111yescharacteristic
343C2×#478C2×C3711yescharacteristic, complemented
344C2×#416C2×C3711yescharacteristic
345#2441C2×C3711yescharacteristic, complemented
346#2339C2×C3711yescharacteristic
347#2095C2×C3711yescharacteristic, complemented
348#2068C2×C3711yescharacteristic, complemented
349#2066C2×C3711yescharacteristic, complemented
350#2026C2×C3711yescharacteristic, complemented
351#1862C2×C3711yescharacteristic, complemented
352#1862C2×C3711yescharacteristic, complemented
353#1854C2×C3711yescharacteristic, complemented
354#1850C2×C3711yescharacteristic, complemented
355#1808C2×C3711yescharacteristic, complemented
356#1802C2×C3711yescharacteristic, complemented
357#1788C2×C3711yescharacteristic
358C2×C37—42no—
359C2×C37—44no—
360C2×C37#243711yescharacteristic
361C2×C37#307611yescharacteristic
362C2×C37#308311yescharacteristic
363C2×C37#326811yescharacteristic
364C2×C37#328311yescharacteristic
365C2×C37#329711yescharacteristic
366C2×C37#331511yescharacteristic
367C22×#41C22×C3711yescharacteristic
368C23×C8C22×C3711yescharacteristic
369C2×#125C22×C3711yescharacteristic
370C2×C4×D4C22×C3711yescharacteristic
371C2×C4×D4C22×C3711yescharacteristic
372C2×#117C22×C3711yescharacteristic
373#478—24no—
374C2×#107C22×C3711yescharacteristic
375C2×#107C22×C3711yescharacteristic
376C2×#107C22×C3711yescharacteristic
377C2×#106C22×C3711yescharacteristic
378C2×C4⋊C8C22×C3711yescharacteristic
379C2×C4⋊C8C22×C3711yescharacteristic
380#416—24no—
381C2×#103C22×C3711yescharacteristic
382C2×#103C22×C3711yescharacteristic
383C2×#103C22×C3711yescharacteristic
384C2×#103C22×C3711yescharacteristic
385C2×#102C22×C3711yescharacteristic
386C2×#102C22×C3711yescharacteristic
387C2×#102C22×C3711yescharacteristic
388C2×#102C22×C3711yescharacteristic
389C2×C22⋊C8C22×C3711yescharacteristic
390#399—21no—
391#396—21no—
392#391C22×C3711yescharacteristic
393#391C22×C3711yescharacteristic
394#389—21no—
395#389C22×C3711yescharacteristic
396#389C22×C3711yescharacteristic
397#387—21no—
398#386—21no—
399#386—21no—
400#384C22×C3711yescharacteristic
401#381—21no—
402#380C22×C3711yescharacteristic
403#380C22×C3711yescharacteristic
404C4×C22⋊C4C22×C3711yescharacteristic
405C2×#95—21no—
406#340C22×C3711yescharacteristic
407#340C22×C3711yescharacteristic
408#340C22×C3711yescharacteristic
409#340C22×C3711yescharacteristic
410#336C22×C3711yescharacteristic
411#336C22×C3711yescharacteristic
412C37#2595611yescharacteristic, direct product factor, Sylow
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—41no—
417C2×#41—41no—
418C2×#41Q8×C3714yes—
419C22×Q8C23×C3711yescharacteristic
420C22×D4—21no—
421C22×D4C23×C3711yescharacteristic
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—21no—
425C23×C4C23×C3711yescharacteristic
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—41no—
429C22×C8C23×C3711yescharacteristic
430C22×C8C23×C3711yescharacteristic
431C22×C8C23×C3711yescharacteristic
432C22×C8C23×C3711yescharacteristic
433#125—22no—
434#125—41no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—41no—
438C4×D4—41no—
439#117—22no—
440#117—41no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4C23×C3711yescharacteristic
448C2×C4⋊C4C23×C3711yescharacteristic
449C2×C4⋊C4C23×C3711yescharacteristic
450C2×C4⋊C4C23×C3711yescharacteristic
451C2×C4⋊C4C23×C3711yescharacteristic
452C2×C4⋊C4C23×C3711yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C3711yescharacteristic
459C2×C22⋊C4D4×C3711yescharacteristic
460C2×C42—21no—
461C2×C42C23×C3711yescharacteristic
462C2×C42C23×C3711yescharacteristic
463#107—22no—
464#107—41no—
465#107—41no—
466#106—22no—
467C4⋊C8—22no—
468C4⋊C8—41no—
469#103—22no—
470#103—22no—
471#103—41no—
472#103—41no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102D4×C3714yes—
477C22⋊C8—22no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95D4×C3711yescharacteristic
487#95D4×C3711yescharacteristic
488C24—21no—
489C24C2×D4×C3711yescharacteristic
490#41—28no—
491#41—44no—
492#41—44no—
493#41—44no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×Q8×C3712yes—
500C2×D4—24no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4C2×D4×C3712yes—
507C2×D4C2×Q8×C3712yes—
508C2×D4#41×C3712yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4C2×D4×C3711yescharacteristic
530C22×C4C2×D4×C3711yescharacteristic
531C22×C4C2×D4×C3711yescharacteristic
532C22×C4C2×D4×C3711yescharacteristic
533C22×C4C2×D4×C3711yescharacteristic
534C22×C4C2×Q8×C3712yes—
535C22×C4#41×C3712yes—
536C22×C4C24×C3711yescharacteristic
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—44no—
549C2×C8C2×D4×C3712yes—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C4⋊C4—81no—
567C4⋊C4C2×D4×C3712yes—
568C22⋊C4—22no—
569C22⋊C4—41no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C23—22no—
581C23—21no—
582C23—22no—
583C23—22no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C22⋊Q8×C3712yes—
594C23C22×D4×C3711yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—41no—
598Q8—41no—
599D4—22no—
600D4—22no—
601D4—22no—
602D4—48no—
603D4C22⋊Q8×C3714yes—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—48no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—84no—
645C2×C4C22⋊Q8×C3712yes—
646C2×C4#135×C3712yes—
647C2×C4C22×D4×C3711yescharacteristic
648C2×C4C22×Q8×C3711yescharacteristic
649C2×C4C2×#41×C3711yescharacteristic
650C2×C4C2×#41×C3711yescharacteristic
651C2×C4H(5,𝔽2)×C3711yescharacteristic
652C2×C4H(5,𝔽2)×C3711yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C22—22no—
658C22—24no—
659C22—22no—
660C22—22no—
661C22—42no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—42no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22C2×C22⋊Q8×C3711yescharacteristic
672C22D42×C3711yescharacteristic
673C22C37×#54611yescharacteristic
674C22C2×#135×C3711yescharacteristic
675C22C37×#57511yescharacteristic
676C22C37×#57611yescharacteristic
677C22C37×#57811yescharacteristic
678C4—22no—
679C4—22no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4C2×C22⋊Q8×C3711yescharacteristic
691C4C37×#54311yescharacteristic
692C4C37×#54611yescharacteristic
693C4C37×#55111yescharacteristic
694C2—42no—
695C2—44no—
696C2C37×#243711yescharacteristic
697C2C37×#307611yescharacteristic
698C2C37×#308311yescharacteristic
699C2C37×#326811yescharacteristic
700C2C37×#328311yescharacteristic
701C2C37×#329711yescharacteristic
702C2C37×#331511yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC22×#41×C37C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C22⋊C4×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C37×#478C2semidirect
3. C37×#2441C2semidirect
5. C37×#2095C2semidirect
6. C37×#2068C2semidirect
7. C37×#2066C2semidirect
8. C37×#2026C2semidirect
9. C37×#1862C2semidirect
10. C37×#1862C2semidirect
11. C37×#1854C2semidirect
12. C37×#1850C2semidirect
13. C37×#1808C2semidirect
14. C37×#1802C2semidirect
305. #25956C37direct (N × H)
343. C2×#478C2×C37semidirect
345. #2441C2×C37semidirect
347. #2095C2×C37semidirect
348. #2068C2×C37semidirect
349. #2066C2×C37semidirect
350. #2026C2×C37semidirect
351. #1862C2×C37semidirect
352. #1862C2×C37semidirect
353. #1854C2×C37semidirect
354. #1850C2×C37semidirect
355. #1808C2×C37semidirect
356. #1802C2×C37semidirect
412. C37#25956direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C37×#4782
C2×C37×#4162
C37×#24412
C37×#23392
C37×#20952
C37×#20682
C37×#20662
C37×#20262
C37×#18622
C37×#18542
C37×#18502
C37×#18082
C37×#18022
C37×#17882
#2595637